Details

Time bar (total: 14.5s)

sample48.0ms

Algorithm
intervals
Results
27.0ms256×body80valid

simplify1.1s

Counts
1 → 1
Iterations

Useful iterations: 3 (186.0ms)

IterNodesCost
044173
1132173
2502109
3204079
done500079

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 0.2909738639 (* x x))
0.1b
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
0.1b
(* (* x x) 0.0001789971)
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log add-cbrt-cube
19×pow1
13×*-un-lft-identity
12×add-sqr-sqrt
11×flip3-+ flip-+
10×prod-exp cbrt-unprod
9×add-cube-cbrt pow-prod-down
8×frac-add
7×associate-*r*
6×associate-*r/ associate-*l/ associate-/r/ associate-/l/
5×associate-*l*
4×times-frac associate-/r* add-log-exp
3×*-commutative unswap-sqr
2×cbrt-undiv div-exp distribute-lft-out
1×distribute-rgt-in frac-2neg distribute-lft-in clear-num div-inv associate-/l*
Counts
4 → 96
Calls
4 calls:
7.0ms
(* 0.2909738639 (* x x))
13.0ms
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
8.0ms
(* (* x x) 0.0001789971)
249.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* 0.2909738639 (* x x))
91.0ms
(* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))
38.0ms
(* (* x x) 0.0001789971)
274.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))

simplify1.7s

Counts
108 → 108
Iterations

Useful iterations: 2 (650.0ms)

IterNodesCost
02664803
19004583
245933899
done50003899

prune679.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ 0.15298196345929327 (pow x 5))
0.2b
(/ 0.2514179000665375 (pow x 3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
43×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
19×associate-/r*
12×add-exp-log cube-prod
8×sqr-pow
6×div-exp add-cbrt-cube associate-/l*
4×cube-mult unpow3
2×pow1 cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv add-log-exp
Counts
2 → 110
Calls
2 calls:
4.0ms
(/ 0.15298196345929327 (pow x 5))
5.0ms
(/ 0.2514179000665375 (pow x 3))

series93.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(/ 0.15298196345929327 (pow x 5))
41.0ms
(/ 0.2514179000665375 (pow x 3))

simplify481.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (127.0ms)

IterNodesCost
01731234
13131045
211451013
done50001013

prune245.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) 0.0001789971)
1.9b
(exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))))
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
41.5b
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
21×pow1
20×add-exp-log
14×add-cbrt-cube
12×*-un-lft-identity flip3-+ flip-+
9×add-sqr-sqrt pow-prod-down
8×add-cube-cbrt associate-*r/ frac-add
7×prod-exp
6×exp-prod associate-*l/ associate-/r/ log-pow associate-/l/
4×log-div times-frac associate-/r* cbrt-unprod add-log-exp
3×rem-log-exp associate-*r*
2×cbrt-undiv log-prod exp-diff div-exp distribute-lft-out
1×frac-2neg associate-*l* exp-sum clear-num *-commutative div-inv rem-exp-log associate-/l* unswap-sqr
Counts
4 → 87
Calls
4 calls:
8.0ms
(* (* x x) 0.0001789971)
29.0ms
(exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))))
1.2s
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
9.0ms
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (* x x) 0.0001789971)
92.0ms
(exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x))))))
271.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
146.0ms
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

simplify1.5s

Counts
99 → 99
Iterations

Useful iterations: 2 (443.0ms)

IterNodesCost
02854986
19154663
246193975
done50003975

prune725.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

30.8b
(sqrt (* (* x x) 0.0001789971))
30.8b
(sqrt (* (* x x) 0.0001789971))
32.1b
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
41.5b
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
22×pow1
15×add-exp-log
11×flip3-+ flip-+
10×*-un-lft-identity
9×pow-prod-down add-cbrt-cube
8×frac-add
6×add-sqr-sqrt add-cube-cbrt sqrt-pow1 associate-*r/ associate-*l/ associate-/r/ associate-/l/
4×times-frac prod-exp associate-/r* add-log-exp
3×rem-log-exp log-pow
2×cbrt-undiv log-div pow1/2 div-exp sqrt-prod distribute-lft-out
1×log-prod frac-2neg clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 75
Calls
4 calls:
6.0ms
(sqrt (* (* x x) 0.0001789971))
6.0ms
(sqrt (* (* x x) 0.0001789971))
1.2s
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
9.0ms
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

series569.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(sqrt (* (* x x) 0.0001789971))
34.0ms
(sqrt (* (* x x) 0.0001789971))
350.0ms
(/ (* (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (sqrt (* (* x x) 0.0001789971)) (sqrt (* (* x x) 0.0001789971))))) (+ (* (pow x 6) 0.0072644182) (+ 1.0 (* (* x x) (+ 0.1049934947 (* 0.0424060604 (* x x))))))) x) (+ (+ (* (pow x 6) 0.0694555761) (+ (exp (log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))) 1.0)) (+ (* (* 2.0 (pow (* x x) 6)) 0.0001789971) (* (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945))))))
144.0ms
(log (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))))

simplify1.2s

Counts
87 → 87
Iterations

Useful iterations: 2 (311.0ms)

IterNodesCost
02635128
18684474
241443796
done50003796

prune751.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.6b

bsearch423.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
703.4866696794237
7
-1162.6651869185068
-5.7596417613087905
-708.5573543956083

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
066127
195113
done95113

end0.0ms

sample1.0s

Algorithm
intervals
Results
932.0ms8000×body80valid